Apparent slip of shear thinning fluid in a microchannel with a superhydrophobic wall

The peculiarities of simple shear flow of shear thinning fluids over a superhydrophobic wall consisting of a set of parallel gas-filled grooves and solid stripes (domains with slip and stick boundary conditions) are studied numerically. The Carreau-Yasuda model is used to provide further insight into the problem of the slip behavior of non-Newtonian fluids having a decreasing viscosity with a shear rate increase. This feature is demonstrated to cause a nonlinear velocity profile leading to the apparent slip. The corresponding transverse and longitudinal apparent slip lengths of a striped texture are found to be noticeably larger than the respective effective slip lengths of Newtonian liquids in microchannels of various thicknesses and surface fractions of the slip domains. The viscosity distribution of the shear thinning fluid over the superhydrophobic wall is carefully investigated to describe the mechanism of the apparent slip. Nonmonotonic behavior of the apparent slip length as a function of the applied shear rate is revealed. This important property of shear thinning fluids is considered to be sensitive to the steepness of the viscosity flow curve, thus providing a way to decrease considerably the flow resistance in microchannels.